Supersymmetric KP Systems Embedded in Supersymmetric Self-Dual Yang-Mills Theory

TL;DR

This paper demonstrates how N=1 supersymmetric KP equations can be embedded into N=1 supersymmetric self-dual Yang-Mills theories through dimensional reduction, leading to new insights and solutions in supersymmetric integrable systems.

Contribution

It establishes a novel embedding of supersymmetric KP systems into supersymmetric Yang-Mills theories and proposes conjectural N=2 SKP equations, expanding the understanding of supersymmetric integrable models.

Findings

Embedding of N=1 SKP into supersymmetric Yang-Mills theories.

Derivation of three-dimensional supersymmetric Chern-Simons theories.

Exact solutions including fermionic fields for these systems.

Abstract

We show that $~N=1$~ {\it supersymmetric} Kadomtsev-Petviashvili (SKP) equations can be embedded into recently formulated $~N=1$~ self-dual {\it supersymmetric} Yang-Mills theories after appropriate dimensional reduction and truncation, which yield three-dimensional supersymmetric Chern-Simons theories. Based on this result, we also give conjectural \hbox{$N=2~$} SKP equations. Subsequently some exact solutions of these systems including fermionic fields are given.